Question

Prove that 3root5 is an irrational number.​

Answer 1

Step-by-step explanation:

Let us assume that 3 + √5 is a rational number. Here, {(a - 3b) ÷ b} is a rational number. But we know that √5 is a irrational number. So, {(a - 3b) ÷ b} is also a irrational number.

Answer 2

Given:-

• A number 3√5

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To Prove:-

• 3√5 is an irrational number

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Proof:-

Let the 3√5 is an rational number in the form of p/q where p and Q are integers and q ≠ 0.

➢ Now,

As we Assume:

➟ 3√5 = p/q

➟ √5 = p/3q

➢ Here, p, q and 3 are integers.

So, p/3q is a rational number

➢ And as,

L.H.S. = R.H.S.

So, √5 is also equals to rational number.

➢ But as we know that √5 is an irrational number.

So , here is a contradiction;

➢ Hence,

Hence,Our assumption is wrong.

➢ So,

So,3√5 is an irrational number.

Hence,

Proved✔

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